Question

In the given figure:​ (ii) If $\angle BOC=\angle DOC={34}^{\circ }$ and $\angle AOD={120}^{\circ }$ ; find angle AOB and angle AOC.

Answer 1

Given:$\angle BOC=\angle DOC={34}^{\circ }$,
$\angle AOD={120}^{\circ }$

To find :$\angle AOB\text{and}\angle AOC$



$\because$ $\angle AOD={120}^{\circ }$

$\angle AOB+\angle BOC+\angle DOC={120}^{\circ }$[from figure]

$\angle AOB+{34}^{\circ }+{34}^{\circ }={120}^{\circ }$ [given]

$\angle AOB={120}^{\circ }-{68}^{\circ }$

$\therefore$ $\angle AOB={52}^{\circ }$

Also, $\angle AOC=\angle AOB+\angle BOC$

$\angle AOC={52}^{\circ }+{34}^{\circ }=\angle AOC$

Hence,$\angle AOC={86}^{\circ }$ and $\angle AOB={52}^{\circ }$.